In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a 10 known time and location, the recorded data can be processed by a computer in known ways to produce an image of the subsurface. The image thus presence of valuable hydrocarbons.
Seismograms are commonly recorded as digital samples representing the amplitude of received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into an array (t-x) with each sample in the array representing the amplitude of the seismic signal as a function of time (t) and horizontal distance (x). When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principal tool which the geophysicist studies to determine the nature of the earth's subsurface formation. Before an array of seismic samples or traces can be converted into a seismic section for interpretation by geophysicists, however, the array must be extensively processed to remove coherent noise and make reflection events discernable.
Source-generated coherent noise has received much attention because it can overwhelm the seismic record. This leads to severe deterioration of data quality. Such source-generated noise includes ground roll and air waves in the case of land data, and energy propagating as modes trapped in the water and near-surface layering in the marine case. Also, coherent scattered energy is often observed both in land and marine data. Another type of coherent noise is encountered in marine surveys when two vessels are acquiring seismic data simultaneously in the same general area. A shot from one vessel enters the recording of the other vessel often at oblique angles. In vertical seismic profiling and cross-borehole seismic data, strong coherent noise results from the propagation of tube waves up and down the borehole. In addition, reflected refractions associated with head waves can be a major source of coherent energy and cause severe deterioration of seismic data quality in some areas. Other coherent noise includes multiples and the like.
Probably the most commonly used technique of removing coherent noise from t-x sections is the f-k (frequency-wavenumber) filter. In f-k filtering the t-x data is transformed to the f-k domain. In this domain the coherent noise often occupies a different portion of the f-k domain than the signals and can be easily removed. In U.S. Pat. No. 4,218,765 to Kinkade, seismic traces are transformed to an f-k array and filtering is performed on the traces in the f-k domain. In U.S. Pat. No. 4,380,059 to Ruehle, multiple reflections are filtered from seismograms by transforming them into an f-k array representing amplitude as a function of frequency and wavenumber. In Ruehle, the f-k array of the seismograms is filtered by weighting all samples with the inverse of the f-k transform of the multiple reflections.
While f-k filtering is a very effective means of attenuating coherent noise from seismic traces, it is not the most optimal method in the sense of optimally preserving signal and rejecting noise. Taper zones between the noise and signal in the f-k domain have to be chosen by the geophysicist. If the taper zone is too small sidelobes will appear in the filtered seismic traces. If the taper zone is too large signal may be removed as well as the coherent noise or the coherent noise will not be significantly removed.
Furthermore, multichannel filters such as the f-k filter require uniform spatial sampling. Seismic data acquired on land frequently suffers from non-uniform spatial sampling. This precludes the application of f-k filtering unless trace interpolation is performed. Quite often the data is not sampled close enough in space to prevent aliasing of noise. Attempts to reject aliased noise using the f-k technique forces the resulting output to be highly band-limited, a very undesirable result. Many times aliased noise cannot be removed because it crosses through the signal region in the f-k domain. Also, multichannel filtering techniques are especially sensitive to channel inequalities.
Probably the most undesirable aspect of the f-k filtering is the `mixing` of the data which is unfortunately inherent in that process, producing an undesirable appearance in the output data. In addition, statics which are present in the data cannot properly be resolved after application of the f-k filter because of the `mixing`.
It is therefore an object of the present invention to remove coherent noise from an array of seismic traces without distorting the reflection signals in the array.